Self-learning finite elements for inverse estimation of thermal constitutive models

In this work, a new methodology for inverse estimation of thermal constitutive models is introduced. This new methodology combines computational intelligence with finite element analysis for solving inverse heat transfer problems. A neural network (NN) representation of thermal constitutive behavior and its implementation in non-linear finite element analysis are presented. The self-learning methodology uses a novel concept for developing material models using experimental data and iterative finite element analyses. The proposed methodology searches for complete thermal constitutive models as opposed to identifying parameters in predetermined functional forms. The application of this new methodology is illustrated using a simulated steady-state heat conduction problem. It was found in simulated experiments that the self-learning finite element method can inversely recover accurate NN representations of thermal constitutive models using simple temperature measurements. Moreover, the method showed stability in the presence of imperfect or noisy data. It is shown that the use of a NN representation of the constitutive model improves the stability of solutions naturally due to the imprecision tolerance of NN.